Identification of cracks and cavities using the topological sensitivity boundary integral equation

The purpose of this communication is to present a novel approach to compute the so called Topological Sensitivity (TS) of any variable or functional in elasticity using Boundary Integral Equations (BIE's), and its use as a tool for identification of defects, by itself or in conjunction with zero-order methods, like Genetic Algorithms. The TS of a cost functional provides a measure of the susceptibility of a defect being at a given location. The main contributions are summarized in the following points: Computation of the TS based on a linearized topological expansion, using Boundary Integral Equations. The TS is computed using only information of the non-damaged domain. The calculation is carried out for circular cavities or straight cracks, but the procedure is extensible to other kinds of defects. It is shown that the topological expansion provides a very accurate tool for estimating the defect sizes, even for very large flaws, relative to the domain size. Applicability of the TS for identification of defects, by itself or associated with Genetic Algorithm. This association is very advantageous since the computational time is dramatically reduced.